Problem 66 - Prealgebra

Question

Divide the decimal by the given power of 10 . \(\frac{849.39}{100}\)

Step-by-Step Solution

Answer

8.4939

Step 1: Understand the division by a power of 10

When a decimal is divided by a power of 10, you can simply move the decimal point to the left by as many zeros as there are in the power. Here, 100 has two zeros, so we'll move the decimal point two places to the left.

Step 2: Move the decimal point

Start with the decimal 849.39. Move the decimal point two places to the left. This shifts the decimal from the end of 849.39 to two positions left, resulting in 8.4939.

Step 3: Write the final result

After moving the decimal point, we get the new decimal value of 8.4939. This is the result of dividing 849.39 by 100.

Key Concepts

Decimal Division

Dividing decimals by powers of 10 is a straightforward process. It involves moving the decimal point rather than performing complex calculations. When we encounter a situation such as \[\frac{849.39}{100}\]we realize that 100 is a power of 10 (i.e., \(10^2\)). This means it has two zeros. The rule of thumb for decimal division by any power of 10 is to count the zeros and shift the decimal point to the left accordingly.

Let's break down the steps:

• For each zero in the divisor (the power of 10), move the decimal point one place to the left.
• In this example, there are two zeros, so we move the decimal point in 849.39 two places left.
• This gives us 8.4939 as the final quotient.

Practicing this technique helps you quickly and accurately perform decimal divisions without the need for a calculator.

Place Value

Place value plays a crucial role in understanding decimal division. It describes the value of each digit in a number based on its position. When dealing with decimal numbers, each position to the right of the decimal point represents a fraction of a whole number.

Here's how place values work in our example, 849.39:

• The 8 is in the hundreds place; it represents 800.
• The 4 is in the tens place; it represents 40.
• The 9 is in the ones place; it simply represents 9.
• Moving to the right of the decimal point, the 3 is in the tenths place, representing 0.3.
• The 9 is in the hundredths place, representing 0.09.

When you divide by a power of 10 and move the decimal point, each digit shifts one place to the left per zero in the divisor. Understanding this concept helps you see how the value of each digit changes during division.

Mathematical Operations

Division is one of the core mathematical operations used to separate a number into equal parts. In mathematics, knowing how to divide by powers of 10 is a fundamental skill that simplifies calculations, particularly with decimals.

Let's consider why this operation is valuable:

• It simplifies work with large numbers by reducing them to smaller, more manageable figures.
• It teaches conceptual understanding of numbers and their magnitude, especially crucial when working with money or measurements.
• Division by powers of 10 echoes in real-life applications; for example, currency conversions and metric calculations require these quick mental adjustments.

Developing efficiency in handling these operations strengthens your arithmetic skills and enhances your overall mathematical fluency.